Computation of dominant ideals
Commutative Algebra
2025-04-17 v1 Combinatorics
Abstract
We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. We first analyze dominant ideals with a fixed least common multiple of generators using combinatorial methods. Then, we adopt a probabilistic approach via the \er\ type model, examining both homogeneous and non-homogeneous cases. This model offers an efficient alternative to exhaustive enumeration, allowing the study of dominance through small random samples, even in high-dimensional settings.
Cite
@article{arxiv.2504.12146,
title = {Computation of dominant ideals},
author = {Anna Maria Bigatti and Nursel Erey and Selvi Kara and Augustine O'Keefe and Sonja Petrović and Pierpaola Santarsiero and Janet Striuli},
journal= {arXiv preprint arXiv:2504.12146},
year = {2025}
}